JB and Michael -
But I will guess that the data come from a high school physics experiment on gravitational acceleration which drops a weight dragging a paper tape through a buzzer with a piece of carbon paper in it. This prints periodic marks on the paper tape. The data x are the distances traveled at successive time points following time zero.
No. It is a body (slider?) that is sliding down an inclined plane on an air cushion. we can determine the position of the slider pretty exactly (the error should be less than 0.01m). The clock starts when we release the body and it stops when the body passes a photo cell.
There are two data sets as we experimented with two different angles between plane table. The measurement of the angles is probably a bit less exact than the measurement of the position.
Here are the two data sets: The positions are in the dx-list and are the same in both experiments: dx-list = c( 1.60, 1.55,1.50,...,0.70) (19 values).
The corresponding dt-lists are
dt-list1 = c(6.44,6.29,6.1,6.09,6.02,5.87,5.68,5.65,5.52,5.43,5.30,5.20,5.01,4.88,4.74,4.61,4.44,4.36,4.12)
dt-list2 = c(3.98,3.86,3.78,3.72,3.65,3.59,3.51,3.45,3.37,3.28,3.22,3.14,3.07,2.96,2.89,2.81,2.74,2.61,2.55)
During the first series of measurements, tha body bumped against a boundary that was fixed on the inclined plane. By bumping against this boundray, the inclined plane, that has a much bigger mass than the body, was slightly pushed and after 15 measurements the position of this boundary changed by 0.01m:
A------------------------------B---C
Here B should be a fixed position and A should be changed. According to our mistake B was changed a bit too. C is a boundary that stops the body from leavinf the air cushion (as those sliding bodies are expensive).
Then, when we took the second series of measurements, I "ordered" a pupil to stop tha body with his hand before bumping against C. And really, it seems to me that the second series is more precise.
I think it's DYNAMITE that you're actually doing this data analysis.
Why? I always do this, but this year I started to involve a bit more statistics. I told about how the method of least squares was an "unbiased estimate" and that also some hypothesis testing is done (when I check whether the points lie on a parabola). The pupils are 16 to 18 years old. They have to draw dx against (dt)^2 as their homework and have to fit in a straight line. This is the way we do linear regression.
It's what I always wanted to do as a high school student, but didn't have the technical background then to carry out. In fact ... come to think of it ... I'm pretty sure I STILL HAVE my high school ticker tapes folded up among my high school papers somewhere, 35 years later, still waiting to be properly analyzed !
From your explanations which follow this point, I do not understand a single word (the termini technici are all unknown to me) but I suspect that I pretty much would like to understand them. Sigh. Probably, I should have to read some work on statistics
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